A336985 Colombian numbers that are not Bogotá numbers.

3, 5, 7, 20, 31, 53, 86, 97, 108, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 211, 222, 233, 244, 266, 277, 288, 299, 310, 323, 334, 345, 356, 367, 389, 400, 411, 413, 424, 435, 446, 457, 468, 479, 490, 501, 512, 514, 536, 547, 558, 569, 580, 591, 602, 613

Offset

1,1

Comments

Equivalently, numbers m that are not of the form k + sum of digits of k for any k (A003052), and that are not of the form q * product of digits of q for any q (complement of A336826).

As repunits are trivially Bogotá numbers, there are not repunits in the data.

A336983, A336984, A336986 and this sequence form a partition of the set of positive integers N*

Links

Table of n, a(n) for n=1..55.

Giovanni Resta, Self or Colombian number, Numbers Aplenty.

Index to sequences related to Colombian or self numbers.

Example

7 is a term because there are not k < 7  such that 7 = k + sum of digits of k, and that are not q such that 7 = q * product of digits of q.
13 is not of the form q * product of digits of q for any q <= 13, so 13 is not a Bogotá number, but 13 = 11 + (1+1) is not Colombian, hence 13 is not a term.
42 is Colombian because there does not exist m < 42 such that 42 = m + sum of digits of m, but as 42 = 21 * (2*1) is a Bogota number, 42 is not a term.

Mathematica

m = 600; Intersection[Complement[Range[m], Select[Union[Table[n + Plus @@ IntegerDigits[n], {n, 1, m}]], # <= m &]], Complement[Range[m], Select[Union[Table[n * Times @@ IntegerDigits[n], {n, 1, m}]], # <= m &]]] (* Amiram Eldar, Aug 26 2020 *)

Prog

(PARI) lista(nn) = Vec(setintersect(setminus([1..nn], Set(vector(nn, k, k+sumdigits(k)))), setminus([1..nn], Set(vector(nn, k, k*vecprod(digits(k))))))); \\ Michel Marcus, Aug 26 2020

Crossrefs

Cf. A003052 (Colombian), A176995 (not Colombian), A336826 (Bogotá numbers), A336983 (Bogotá not Colombian), A336984 (Bogotá and Colombian), this sequence (Colombian not Bogotá), A336986 (not Colombian and not Bogotá).

Sequence in context: A362417 A352710 A163637 * A360929 A228068 A182233

Adjacent sequences: A336982 A336983 A336984 * A336986 A336987 A336988

Keyword

nonn,base

Author

Bernard Schott, Aug 26 2020

Status

approved